Find Which GCSE Higher Maths Topics Are Essential To Success In The GCSE Higher Exams 2024

The education sector has tackled some serious hurdles in recent years, especially regarding exams and assessments for GCSE Higher maths. With the complications of teacher-assessed grades and advanced information behind us, and a return to the conventional GCSE structure and specification, let’s take a look at the key topics you should be focusing on with your Higher exam groups in 2024.

What is the current picture for higher maths?

In 2024, GCSEs will fully revert to their conventional, pre-pandemic structure. In 2023, formula sheets were provided for mathematics, physics, and combined science, serving as a supportive measure for students who faced learning disruptions due to the pandemic.

However, these formula sheets will not be accessible in 2024. Consequently, candidates will once again be required to commit certain formulae to memory.

Maths study beyond GCSE

We need to strike an equilibrium between preparing students for their GCSE mathematics exams and equipping them with skills for future life or study. It’s essential to bear in mind that the objectives of education extend beyond getting students to pass exams – an idea echoed in Ofsted’s latest maths subject report, which expresses concerns regarding the degree to which external exams are driving curriculum planning.

At GCSE level, a school-wide approach may be necessary, collaborating with colleagues to understand what skills are fundamental for success in post-16 study. This will depend on the school’s individual setting and demographic. For example, it may be important to ensure that statistical content (necessary for study of AS/A-level Psychology) is covered, or that students have sufficient algebra and graphing skills to be able to access A Level Sciences. For schools with a high proportion of students who go on to study A-level Maths, a sound grasp of algebra and geometry skills from GCSE is crucial.

This blog focuses on topics and strategies for exam preparation for the new Higher mathematics GCSE and draws upon research and analysis conducted on the all series of Edexcel GCSE maths past papers GCSE higher maths past papers available from Edexcel since June 2017. Please bear this in mind if you use the other exam boards, including AQA, OCR, WJEC, or are sitting iGCSE maths. 

See also: How To Revise For GCSE

We firmly advocate that a comprehensive and well-rounded curriculum should be accessible to all students, and choice of teaching topics should primarily align with their current mathematical attainment. As such, the recommendations in this article should not be used to restrict the scope of teaching content.

However, when preparing for GCSE exams, there are some topics which are frequently and widely assessed across the papers, while others appear less frequently or tend to be assessed in specific ways. It could be advantageous for final exam preparation to reflect these patterns, allowing students more time to focus on skills that typically yield higher marks.

This article looks at the specific topics and approaches you can use to maximise revision time with your Higher students.

Number in higher maths

Key topics

• Procedural work on standard form, HCF and LCM, expressing recurring decimals as fractions, using a calculator and error intervals.
• Crossover between lower and upper bound calculations and compound measures, particularly speed and density.
• Powers and roots, particularly negative and fractional indices, simple laws of indices, rationalising the denominator and application of surd simplification to other topics.
• Significant crossover between error interval and bound calculations and compound measures, particularly speed and density.
• Explaining how a change to a calculation would affect an answer, linking to work on estimation.

Infrequently appearing topics

• Problem-solving or rich problems using HCF, LCM, product of primes, standard form, surds.

Frequently appearing questions 

For me, the key thing in preparing students for the Higher maths papers is ensuring that their basic calculation skills are absolutely watertight. There are significantly fewer marks in the marking scheme on Higher, for carrying out procedural arithmetic calculations. It is expected that students should be able to work quickly, accurately and flexibly with number, including calculating with negatives, fractions, decimals, percentages and ratio. Therefore, when these skills appear in other exam questions, it is crucial that these calculations can be carried out almost automatically.

There are still some easy wins in the Number strand: standard form, HCF and LCM, power calculations (particularly fractional indices), surd manipulation, expressing recurring decimals as fractions, using a calculator and error intervals are all topics assessed in a fairly procedural manner on most papers. More in-depth questions about lower and upper bounds tend to include context, often speed or density calculations.

Don’t miss: 80+ GCSE maths revision guides for Number.

Algebra in higher maths

Key topics

• Basic algebra skills (simplify, expand, factorise, solving equations and inequalities) need to be automatic.
• Algebraic fractions are frequently used to assess a range of algebraic manipulation skills.
• Application of linear and quadratic equations and inequalities to a variety of contexts, particularly perimeter, area and volume.
• Basic graph skills, equation of a straight line, drawing graphs and estimating solutions from a graph.
• Procedural work within sequences and functions, such as quadratic nth term, inverse and composite functions.
• Simultaneous equations, including non-linear, expanding triple brackets, solutions of equations using iteration.
• Gradients and areas, particularly using speed-time and distance-time graphs.

Infrequently appearing topics

• Completing the square
• Gradients and areas (not SDT)
• More challenging multi-step coordinate geometry problems

What should you be teaching based on the paper analysis?

The first thing to note is that many of the topics towards the bottom of the graph above, while infrequently appearing as a main topic in a question, are either assessed embedded in other questions or are assumed knowledge at Higher level. For example, students are fairly unlikely to be asked to plot a linear graph or carry out a procedural substitution, but they are extremely likely to be asked to draw or interpret a quadratic graph, requiring application of substitution and graph-plotting skills.

Further to this, the algebra toolkit of simplifying, expanding and factorising is also assumed knowledge at Higher GCSE and is less likely to be assessed in a standalone question. Many of these skills are embedded within other problems; for example, algebraic fractions feature very highly, allowing for simultaneous assessment of expanding and factorising.

From past exams and specimen papers we can glean that students are much more likely to be asked to procedurally expand triple brackets rather than double brackets, because work on quadratic expressions and equations is more frequently assessed in context. Algebraic proof is generally very challenging due to the fact that many of the questions do not give any scaffolding or hints (such as the algebraic forms needed to complete the proof).

Students must be able to form linear and quadratic equations and inequalities from contexts, as well as being reliably able to solve using an appropriate method. Contexts include perimeter and area problems, nth term expressions and quadratic sequences, probability, and the trigonometric formula for area of a triangle, ½ ab sin C.

Candidates are likely to be asked to solve a system of simultaneous equations with one linear, one quadratic or other non-linear; this is also another opportunity to assess quadratic manipulation skills.

Basic graph skills, such as drawing, using graphs to estimate solutions to equations, and finding equations of parallel and perpendicular lines are really important. There is some nice accessible content in non-linear graphs too, such as matching pictures of different graphs to their equations, or drawing graphs of quadratics and circles. 

A couple of other easy wins here include iteration, which (if it appears) is done in a step-by-step procedural manner, inverse and composite functions, and nth term of a quadratic sequence. It’s also worth mentioning when gradients and areas under curves seems to crop up quite a bit, usually in the context of speed-time or distance-time graphs, and, despite being considered a ‘harder topic’, is procedural and quite accessible.

Don’t miss: 70+ GCSE maths revision guides for Algebra.

Ratio and proportion in higher maths

Key topics

• Proportional reasoning, particularly ratio, assessed throughout the paper, and lack of understanding could limit accessibility of other topics.
• Explicit teaching and modelling of problem-solving in the real-life contexts was presented in percentage questions.
• Plenty of applied work with compound measures, including interweaving with other topics such as volume and surface area.

Infrequently appearing topics

• Standalone standard unit conversions (so far, always squared or cubed units)
• Proportion graphs

Ratio, in particular, appears throughout the Higher papers in a variety of contexts. The standard ‘split into a ratio’ or ‘find a quantity’ is not examined independently, but appears within other questions, often stating key information. For example, angles for a trigonometry problem given as a ratio rather than as values. Without the ability to carry out procedural ratio calculations, many questions become inaccessible. 

As with Foundation tier, there is a clear undercurrent of proportional reasoning throughout the papers, both in typical real-life problem solving contexts, and with more abstract concepts. Students are expected to be able to make connections between topics more readily, such as using exponential formulae to represent compound percentage change.

Compound measures (speed, density and pressure) accounts for nearly 20% of the marks for the entire strand. It has appeared on every series so far, and is a favourite topic for common questions, appearing at the start of the Higher paper. Density frequently appears in combination with volume of 3D shapes.

Don’t miss: 20+ GCSE maths revision guides for Ratio and Proportion.

Geometry in higher maths

Key topics

• Perimeter, area and volume, particularly context-based problems.
• Pythagoras and trigonometry, with focus on problem-solving, double applications of rules, working in 3D or applying to area calculations.
• Clear mathematical reasoning for 2D shape and angle problems, particularly angles in polygons and circle theorems.

Infrequently appearing questions

• Constructions, scale drawings and bearings.
• 3D shape and angle properties.

What should you be teaching based on paper analysis?

One thing I noted from the paper analysis is the large amount of problem-solving based around perimeter, area and volume; there were almost no procedural problems, in favour instead of real-life contexts and unfamiliar abstract situations. As well as ensuring students can reliably apply standard methods, they must be able to flexibly apply these skills to other problems.

As with algebra, some of the topics towards the bottom of the graph above appear infrequently as standalone questions, but are assumed knowledge at Higher level and are embedded in other questions. For example, perimeter and area of rectilinear shapes is unlikely to be assessed as the main topic in a question, but is prior knowledge for volume and surface area topics, and also appears embedded in other questions. 

There was significant crossover with solving equations and inequalities, both linear and quadratic, Pythagoras and trigonometry, and other 2D shape and angle reasoning. Another key area within perimeter, area and volume is using one measure to calculate another – for example, calculating the surface area of a shape given its volume.

Pythagoras and trigonometry was another key area. The majority of these questions had significant elements of problem solving. There was quite a bit of higher level trigonometry, such as sine and cosine rule problems, often requiring a double application, or use of Pythagoras, or some crossover with area calculations.

3D Pythagoras or trigonometry appeared in half of the series.

Constructions, bearings, and scale drawings appeared less frequently. As such, these are topics worth reviewing quickly before the exam period rather than going into considerable depth. Similarly, plans and elevations only appeared on a couple of papers, and questions were procedural and intuitive, so great depth is not required here either.

Speed and density featured heavily within work on units, measurements and drawings, while constructions, bearings and scale drawings appeared less frequently. While I don’t advocate skipping these topics completely, it’s perhaps worth just reviewing quickly before the exam period rather than going into considerable depth.

Similarly, plans and elevations only appeared on a couple of papers, and questions were procedural and intuitive, so great depth is not required here either.

Don’t miss: 125+ GCSE maths revision guides for Geometry and Measure.

Probability in higher maths

Key topics

• Procedural work on combinations, Venn diagrams, tree diagrams.
• Application of fraction and ratio skills to unfamiliar contexts for mutually exclusive events or relative frequency.
• Complex combined event problems for higher-attaining students.

Infrequently appearing topics

• Frequency trees, sample spaces and two-way tables.

What should you be teaching based on the paper analysis?

Like Foundation, a fair proportion of probability is assessed in procedural ways, although there are some challenging problems around independent events and conditional probability for the most able candidates.

Procedural work on ‘newer’ topics such as Venns and combinations is would be valuable, as these topics seem to appear frequently, and have so far been assessed in similar-looking questions. There were no questions with pre-drawn frequency trees (although candidates could have chosen to use these for non-structured questions), with focus almost exclusively on tree diagrams.

Don’t miss: 35+ revision guides for Probability.

Statistics in higher maths

Key topics

• Presenting data: drawing and interpreting cumulative frequency graphs, box plots, histograms, frequency polygons.
• Estimating the mean and calculating averages and range from charts and graphs.

Infrequently appearing topics

• Charts for categorical or discrete data (bar, pictogram, pie).
• Time series graphs or analysing time series data.
• Stem and leaf plots.

What should you be teaching based on the paper analysis?

In statistics, the emphasis is more heavily on presenting data using charts and graphs rather than calculating averages or spread processing data, with equal focus on drawing or completing charts and graphs, and interpreting or critiquing existing representations. Cumulative frequency graphs, box plots, frequency polygons appear frequently; scatter graphs usually include a drawing and interpreting component.

Processing data usually involves estimation of the mean from a table, or reading information from a pre-drawn chart or graph, such as calculating the interquartile range from a given box plot. Data collection and sampling doesn’t appear on every series;, but this has either usually been assessed in a standard ‘stratified sample-style’ question, whichand doesn’t need a great deal of depth, or more recently as capture-recapture.

Don’t miss: 40+ revision guides for Statistics.

What topics appear in the common questions on the higher tier?

On each paper, there are approximately 7-8 questions which appear on both tiers of paper – towards the top end of the Foundation paper, and as the first few questions on Higher. These questions are often broken into parts, and carry nearly a third of the overall marks per paper.

The most frequently appearing common questions are on the following topics:

• Quadratic graphs
• Compound measures
• Standard form
• Scatter graphs
• HCF, LCM and PPF
• Pythagoras and trigonometry in RA triangles
• Writing as a ratio
• Ratio and fraction links
• Combining ratios
• Laws of indices
• Sets and Venns
• Angle facts and properties
• Fraction calculations

For more detailed analysis of the crossover portion of Edexcel’s exam papers, see my analysis piece: Supercharge Your Higher Maths Lessons.

For a more detailed discussion of tiers of entry and what topics to teach borderline Higher students, see The GCSE Maths Topics Your Year 10 And Year 11 Should Revise.

Higher maths teaching strategies

Making connections

One essential element of exam preparation for the higher papers is to ensure that students are familiar with connections within the content. As already discussed, key topics here include ratio and percentages, linear and quadratic equations and inequalities, perimeter, area and volume, and Pythagoras and trigonometry.

Students need plenty of exposure to questions requiring applications of multiple topics, and plenty of opportunity to work on these problems in a collaborative way as a class. Many schemes of work devote most, if not all, of Year 11 to GCSE maths revision resources and past exam paper preparation; this is an ideal time to explore links and show students the variety of contexts their skills can be applied to.

Developing resilience

It is also important to develop resilience and a willingness to have a go at most or all questions. We must remember that a significant proportion of the Higher paper is aimed at grade 7-9 candidates, and that some of the multi-step problems will be incredibly challenging for some candidates.

That said, we need to model and develop strategies for achieving maybe the first couple of marks on a 5-mark question. For example, in a multi-step problem involving a double application of trigonometry, maybe the student can get the first couple of marks for applying right-angled triangle trigonometry correctly. 

Low stakes practice

Continual, low-stakes formative assessment (regular mini-quizzes, perhaps using the starting portion of the lesson) is more crucial than ever for identifying gaps in learning. GCSE intervention strategies need to be in place from September to pick up those students who are already struggling. 

Read more: GCSE grade boundaries

Third Space Learning’s GCSE online maths courses are designed to cover the entire GCSE maths curriculum. Each lesson provides step-by-step worked examples, multiple-choice practice questions designed to address misconceptions, practice exam questions with student-friendly mark schemes, learning checklists taken from the national curriculum and free, printable GCSE maths worksheets. By working through these lessons students are able to practise and know how to revise the GCSE mathematics content in order to develop mathematical fluency and increase their confidence. 

Read more:

• The Most Impactful GCSE Maths Topics
• Edexcel Maths GCSE Past Papers
• How to Revise: 20 Proven Revision Techniques

Third Space Learning offers one-to-one online intervention to help students prepare for the maths GCSE exam. Assessing the needs of each individual student, our intervention lessons are designed to plug the gaps in students’ learning and build confidence going into the GCSE maths exam.Third Space Learning also provides a wide variety of free resources and worksheets available on our website to help students with maths revision.